A COMMENT ON IMAGE DETECTION AND THE DEFINITION OF LIMITING MAGNITUDE

A useful operating definition for limiting magnitude in CCD photometry is the level at which the completeness of detection drops to 50 percent. If the detection threshold is defined as Q times the standard deviation of the sky noise, then it can be shown that the Q value needed to reach a given limiting magnitude, or signal-to-noise ratio (SNR), varies inversely with the scale of the detector. In addition, the highest achievable threshold Q (lim) for any image scale is numerically equal to the SNR of the stars just at the 50 percent completeness limit.